Quantum cryptography transmission method and system

ABSTRACT

Encoding digital data intended for transmission by a particle flow of single particles, includes: encoding digital data on a parameter x of said particle flow, wherein the parameter x has a conjugated parameter y of said particle flow; and ensuring that said parameter x and said conjugated parameter y are in a minimum state (Δx. Δy=1).

The invention concerns the field of cryptography.

Through the use of cryptography, a message can only be read by itsrecipient. A key is used to encrypt the message. The owner of the key isthe only person who can read the message received.

The encryption key must therefore be transmitted by the sender to therecipient of the encrypted message. Transmission is carried out suchthat only the recipient of the encrypted message receives thisencryption key. Interception by a third party of the encryption key isdetected by the sender or the recipient. Consequently, the encryptionkey detected as intercepted is not used for the message encryption.

The principle of transmitting encryption keys is used, for example, inquantum cryptography. It consists of using physical properties toguarantee the integrity of a received encryption key.

The encryption key consists of a bit sequence. The encryption key isencoded on a flow of particles. The particles may be, for example,photons or may be other types of particles. In the case where theparticles are photons, a time shift of a pulse on a light flow isassociated with each bit. The light flow, encoded in the time domain andcomprising a flow of photons, is then attenuated. The probability ofdetecting two photons associated with the same bit is then negligible.

The transmitter (Alice) can encode the encryption key on twononorthogonal states. The pulses sent by Alice have a time width of ΔTand amplitude such that the probability of detecting a photon throughoutthe pulse duration is equal to one (state with one photon) orsufficiently low so that the probability of detecting two photons isnegligible faced with the probability of detecting one (coherent state).

In reception, the detection states are chosen in a base with two states.These two detection states are orthogonal respectively to each state ofthe base used by the sender. During transmission, the transmission anddetection states are chosen independently of each other.

If the states chosen by the transmitter and the receiver are orthogonal,the detection probability is zero. The measurement result is certain,there is no ambiguity. If they are not orthogonal, there are twopossible measurement results since the probability of detecting thephoton is 0.5. If the photon is detected, it is certain that thetransmitter state is at 45° to the receiver state. There is noambiguity. Irrespective of the configuration, there is always apossibility of not detecting the photon. This non detection of thephoton makes deducing the choice of transmitter shift, using thereceiver state, ambiguous. This ambiguity concerning the shift is usedin quantum cryptography.

Detection of the photon is a point process which can occur at any timeduring the pulse. The spy (Eve) can, for example, measure all the pulsessent by Alice. She has a detector of quantum efficiency equal to one.For each pulse transmitted by Alice, she detects the correspondingphoton. If she can instantaneously retransmit to the receiver Bob pulsewith one photon but time width of ΔT′ shorter than that sent by Alice,she can also read the information without being unmasked as shown inFIG. 1.

Bob then in fact receives shorter pulses but he cannot detect this. Theprobability of detecting a photon is the same as when the pulses wouldnot have been intercepted. In addition, their time position isconsistent with the encoding imposed by Alice. Half of the pulsesretransmitted by Eve result in exploitable information (unambiguous) andthe other half in ambiguous results. When Alice and Bob compare the keyportions, they will be unable to detect an increase in the error ratewhich would indicate the presence of a spy.

Consequently, if the pulse duration is not fixed, a third party, the spy(Eve), can measure the information transmitted by the transmitter(Alice) and return an equivalent signal to the receiver (Bob) withoutbeing detected. Eve then has a copy of the information, without beingunmasked. This type of spying is difficult to carry out in practice butthe possibility of this principle cannot be excluded.

This invention proposes a means of preventing this type of spying byusing a minimum state. This minimum state is one where the product ofthe uncertainty of the encoding parameter and its conjugated parameteris equal to its minimum value.

This invention concerns a method to encode digital data on one of theparameters x of a particle flow intended for transmission such that theprobability of transmitting two particles per period is negligible,wherein the parameter x and its conjugated parameter are in a minimumstate (Δx. Δy=1).

The invention proposes a method of decoding digital data encoded suchthat two conjugated parameters x and y in the encoded particle flow arein a minimum state, the probability of detecting two particles perperiod being negligible, wherein it comprises at least:

-   -   a filtering step used to separate the particles received        satisfying the relation Δx₁.Δy₁≧1 but where Δx₁≠Δx or Δy₁≠Δy (Δx        and Δy fixed) from the particles characterized Δx and Δy, and    -   a decoding step as such to decode particles satisfying the        minimum state relation.

The decoding method is implemented by a decoder of digital data encodedsuch that two conjugated parameters x and y in the encoded particle floware in a minimum state, the probability of detecting two particles perperiod being negligible, wherein the decoder comprises at least:

-   -   a filter used to separate the particles received satisfying the        relation Δx₁.Δy₁≧1 but where Δx₁≠Δx or Δy₁≠Δy (Δx and Δy fixed)        from the particles characterized Δx and Δy, and    -   an elementary decoder receiving only those particles satisfying        the minimum state relation.

The advantages and features of the invention will be clearer on readingthe following description, given as an example, illustrated by theattached figures representing in:

FIG. 1, the representation of the pulses transmitted by Alice and Eveaccording to the state of the art technology.

FIG. 2, a block diagram of the transmission system implementing theinvention,

FIG. 3( a), a first variant of the decoder according to the invention,

FIG. 3( b), a second variant of the decoder according to the invention,

FIG. 4, a transmission system with a “interferometer” structureaccording to the invention.

The parameters satisfying the minimum state chosen as an example in thefigures and the description are the time width ΔT of the pulse carryingthe information and its conjugate: the spectral width Δv of this pulse.The principles and system can be applied for all types of encodingparameter x (time width, spectral width, polarization, position, pulse,beam size, beam divergence, etc.) and its parameter y such that theysatisfy the minimum state relation Δx.Δy=1.

On FIG. 1, the pulses of time width ΔT are transmitted by Alice. If Evedetects a photon, she can retransmit a pulse of shorter time width ΔT′so that Bob cannot detect the interception. The amplitudes of the pulsestransmitted by Alice and Eve are such that the probability of detectinga photon is the same for both pulse types. Depending on the instant ofdetection, the pulse transmitted by Eve carries, or not, theinformation.

To prevent the type of spying described above and shown on FIG. 1, thepulses are also defined in the frequency space. The pulses transmittedby Alice are characterized by a time width ΔT and a spectral width Δvwhose product is always greater than a constant of approximate valueone: ΔT′Δv≧1. This relation is similar to the Heisenberg uncertaintyrelations which connect two conjugated parameters x and y: Δx′Δy≧h. Whenthis relation becomes an equality, we obtain a minimum state. Theuncertainty on one of the conjugated variables is directly the inverseof the uncertainty on the other conjugated variable. These variables maybe, for example, the position p_(z) and the pulse z. The equivalent inthe time-frequency space is called the “Fourier Transform” pulse. Itsatisfies the relation ΔT′Δv=1.

FIG. 2, shows the block diagram of a transmission system implementingthe invention. Encoder 1 supplies, therefore, a flow of pulses in aminimum state carrying the information to be transmitted on the value ofthe pulse shift with respect to the initial instant of the period.

This type of encoder may include:

-   -   [ENCODER A] Either an encoded pulse source 11 ⁺² (for example, a        laser generating a discontinuous laser beam of pulses more or        less shifted according to the encoded data and satisfying the        minimum state relation),    -   [ENCODER B] Or a controllable delay gate 13 receiving a particle        pulse flow satisfying the minimum state relation and from a        pulse source 11 ⁺²,    -   [ENCODER C (case illustrated in FIG. 2)] Or an encoded pulse        chopper (not shown) chopping pulses satisfying the minimum state        relation with the appropriate time shift depending on the data        to be encoded at a frequency Tb in a continuous beam from a        laser,    -   [ENCODER D] Or an encoded pulse chopper chopping pulses        satisfying the minimum state relation at frequency Tb in a        continuous beam from a pulse particle source 11 ⁺² then a        controllable delay gate 13 shifting the pulses more or less with        respect to the initial instant of the period depending on the        data to be encoded.

In the example shown in FIG. 2, the encoder 1 includes a pulse particlesource 11 ⁺² (mode-locked laser, for example) and a delay gate 13 suchthat the encoded pulses satisfy the minimum state relation. The encodedparticle flow supplied by the encoder 1 is then attenuated by theattenuator 2 before being transmitted on a channel. This channel isknown as a quantum channel since the probability that two particles aretransmitted on the channel per period is negligible or the probabilitythat a single particle is transmitted on the channel per period is equalto 1. The attenuator 2 proposed by FIG. 2 includes a half-wave plate 21followed by a polarizer 22 supplying a “key” beam CLE on the quantumchannel. In addition, the polarizer can supply a second, more intensebeam. This secondary “sync” beam can be used as a reference tosynchronize the transmitter and receiver clocks of the quantumcryptography transmission system. The receiver includes at least onedecoder 3 receiving the “key” beam CLE. This decoder 3 is, possibly,synchronized with the transmitter using the secondary “sync” beam.

If the time width ΔT and the spectral width Δv of the pulses transmittedsatisfy the minimum state relation Δv.ΔT=1, a first variant of thedecoder 3 proposed by FIG. 3( a) can be used. The photons of the “key”quantum signal CLE received are filtered by a filter of spectral widthΔv. The photons of spectral width Δv are observed by the photon counter31′ activated on the observation windows on which the value of thetransmitted bit is certain (one window for the bits of value “0” and onewindow for the bits of value “1”).

On FIG. 3 b, the photons reflected by the filter Δv are also counted bya photon counter 31″. The comparator 32 checks whether the number N_(Δf)of reflected photons is greater to much greater than the number N_(Δv)of photons observed in a first and a second observation window. If thisis the case, the decoder 3 decides that the data transmitted has beenintercepted by a third party. Otherwise, depending on whether the photoncounter 31′ detects a photon in one or other of the observation windows,the decoder 3 decides whether a bit of value “0” or “1” has beentransmitted. Lastly, if the photon counter 31′ does not detect anyphotons in either observation window, the decoder 3 decides that thereis non-reception. It cannot determine whether this non-reception is dueto poor quality transmission or to interception by a third party.

Pulses close to the minimum state relation can be produced, for example,by mode-locked lasers 11 ⁺² in an encoder 1. The time shifts areproduced outside the laser with a delay gate 13. The use of pulsesproduced by mode-locked lasers 11 ⁺² has significant practicalconsequences.

Typically in fact, the pulse durations are between 10 ps and 100 fs.These values are much less than the response times of the existingphoton counters (31′) (typically 1 ns). It is then impossible todistinguish between a pulse shifted and a pulse not shifted. Thisfunction can be carried out by an electrically controlled gate (notshown) located in front of the photon counter (31′). The possibility ofproducing this type of gate largely depends on the response timesobtained with the technology used, for example: 10 GHz with anelectro-optical modulator.

The pulses satisfying the minimum state relation in the time-frequencyspace protect against this type of spying described by FIG. 1. In fact,Eve intercepts the pulses sent by Alice and retransmits pulses of timewidth T′ and spectral width Δv′ which must also satisfy the relationΔT′.Δv′=1 so that the probability of detecting a photon remains thesame. If the time width T′ is much smaller than T, then the spectralwidth Δv′ is necessarily larger than Δv. To detect whether the durationsof the pulses transmitted by Eve have been modified, a filter of widthΔv is simply placed in front of Bob's photon counter as shown on FIG. 3(b). Most photons transmitted by Eve will then be reflected. By placing,for example, a second photon counter on the path of the reflected beam,the counting rate on this counter will suddenly increase when Evetransmits pulses shorter than those expected by Bob. The filter can beproduced, for example, with an interference filter or a Fabry-Pérotfilter with adjustable spacing to choose the spectral passband.

If the pulses used are too short with respect to the gate switchingtime, an interferometer can be used between the transmitter and thereceiver as shown on FIG. 4. A pulse particle source 11 ⁺² generates theparticle flow as a train of pulses of time width ΔT and frequency Tb. Inthis case, the delay gate 13 includes the separating element of theinterferometer. The particle flow is therefore split into two parts senton the two arms of the interferometer. In one arm, the delay gate 13may, for example, transmit or not the pulse in a delay line of durationΔT/2 (if t0=0, t1=T/2) depending on the data to be encoded. The particleflows are attenuated on the two arms by the attenuator 2 before beingtransmitted as “key” signal. The attenuator may, for example, use thesecondary flow as “sync” synchronization signal to synchronize thetransmitter with the receiver. The decoder 3 then transmits or not thepulse of the other interferometer arm into a delay line of identicalduration (ΔT/2 for example). If the delay gate 13 and the decoder 3 havechosen the same delay 0 or ΔT/2, then the probability of detecting aphoton is 100% in one of the output channels (channel a) and zero in theother channel (channel b). If the delay gate 13 and the decoder 3 havechosen different delays, then the probability of detecting a photon is50% in each channel. The fact that the counter 31′ detects a particle inchannel b is used to determine with 100% probability the delay which waschosen by the delay gate 13. The particle counter 31′ is placeddownstream from a filter for the particles of spectral width Δv or may,for example, be replaced by the device shown on FIG. 3( b) if the pulsesgenerated have minimum state.

The encoding/decoding systems and methods using the minimum staterelation for quantum cryptography have been described above forparticles with time encoding. The conjugated parameter is then thespectral width of the pulse carrying the information to be transmitted.It is therefore possible to separate by simple filtering on theconjugated parameter the transmitted particles which do not satisfy theminimum state relation.

The use of time width and spectral width parameters is only an exampleof realization. Generally, all types of parameter x (time width,spectral width, polarization, position; pulse, beam size, beamdivergence, etc.) can be used to carry the information to betransmitted. The invention is then based on the fact that this parameterx and its conjugated parameter y (respectively: spectral width, timewidth, conjugated parameter of the polarization, pulse, position, beamdivergence, beam size, etc.) satisfy the minimum state relation Δx′Δy=1on transmission. On reception, it is then easy to separate the particlessatisfying the minimum state relation by filtering according to theconjugated parameter y. The filtering can be used to separate theparticles received satisfying the relation Δx₁.Δy₁≧1 but where Δx₁≠Δx orΔy₁≠Δy (Δx and Δy fixed by the encoder and known a prior by the decoder)from the particles characterized Δx and Δy.

1. A method to encode digital data intended for transmission by aparticle flow of single particles, comprising the steps of: encodingdigital data on a duration ΔT of said particle flow, and the duration ΔThas a conjugated parameter Δv that is a spectral width of said particleflow; and ensuring that said duration ΔT and said conjugated parameterΔv are in a minimum state (ΔT.Δv=1), wherein the encoding methodcomprises the conversion of the sequence of K bits of digital data intoa train of K pulses of particle flows of duration ΔT and spectral widthΔv satisfying the minimum state relation ΔT.Δv=1, whose frequency Tb, ispredetermined knowing that each of the K pulses being shifted or not intime such that the k^(th) pulse is shifted by a duration t0 respectivelyt1, with respect to the initial instant of the period depending on thevalue “0”, respectively “1” of the k^(th) bit, where k is an integersuch that 0≦k<K and the shifts t0 and t1 are such that 0≦t0,t1≦Tb−ΔT and0<1t1−t01<ΔT.
 2. A digital data encoder for encoding data on a particleflow of single particles intended for a particle transmitter, thedigital data encoder is configured to encode said digital data on aduration ΔT of said particle flow, the duration ΔT has a conjugatedparameter that is the spectral width Δv of said particle flow, and thedigital data encoder comprises a device configured to control theduration ΔT to ensure that the duration ΔT and the conjugated parameterΔv are in a minimum state (ΔT.Δv=1), wherein: the encoder can be used toconvert the sequence of K bits of digital data into a train of K pulsesof duration ΔT, and spectral width Δv, satisfying the minimum staterelation ΔT.Δv=1, whose frequency Tb, is predetermined knowing that eachof the K pulses being shifted or not in time such that the k^(th) pulseis shifted by a duration t0 respectively t1, with respect to the initialinstant of the period depending on the value “0”, respectively “1” ofthe k^(th) bit, where k is an integer such that 0≦k<K and the shifts t0and t1 are such that 0≦t0,t1≦Tb−ΔT and 0<1t1−t01<ΔT.
 3. A method ofdecoding encoded digital data encoded on a single particle flow havingtwo conjugated parameters that are a duration ΔT and a spectral width Δvin a minimum state, the method comprising: a filtering step used toseparate the particles received having duration ΔT₁ and spectral widthΔv₁, and satisfying the relation ΔT₁.Δv₁≧1 but where ΔT₁≠ΔT or Δv₁≠Δv(ΔT and Δv fixed) from particles having duration ΔT and spectral widthΔv, and a decoding step as such to decode particles satisfying theminimum state relation (ΔT.Δv=1), wherein: the time width ΔT of thepulse is shifted or not depending on the value of the bits to be encodedand the spectral width Δv thereof, where Δt=ΔT−1t1−t01, the decodingthen comprising: the filtering step which is used to separate theparticles of spectral width Δv from the other particles, and thedecoding step which comprises: observation of the flow of particlesreceived on or two time windows for each bit reception period ofduration Tb, if t0<t1, the first time observation window starts atinstant t0(inclusive) and ends at instant t1 (exclusive), the secondobservation window starts at instant t1+Δt (exclusive) and ends atinstant t1+T (inclusive), if t1<t0, the first time observation windowstarts at instant t1 (inclusive) and ends at instant t0 (exclusive), thesecond observation window starts at instant t0+Δt (exclusive) and endsat instant t0+T (inclusive), detection of particles in the timeobservation window(s) generates: a bit of value “0”: if t0<t1, when aparticle is detected in the window starting at t0 of period k, if t1<t0,when a particle is detected in the window starting at t0+Δt of period k,a bit of value “1”: if t1<t0, when a particle is detected in the windowstarting at t1 of period k, if t0<t1, when a particle is detected in thewindow starting at t1+Δt of period k, a signal indicating an ambiguityon the bit value if no particle was detected in the first and the secondobservation window, and/or the count of the number N_(Δv) of particlesreceived of spectral width equal to Δv, the count of the number N_(Δf)of particles received of different spectral widths Δf (Δf≠Δv) and acomparison of these two numbers N_(Δv) and N_(Δf) such that ifN_(Δv)<<N_(Δf), the interception of particles by a third party isindicated;
 4. A decoder of encoded digital data, encoded on an encodedsingle particle flow having two conjugated parameters that are aduration ΔT and a spectral width Δv in a minimum state, wherein thedecoder comprises: a filter used to separate the particles receivedhaving duration ΔT₁ and spectral width Δv₁, and satisfying the relationΔT₁.Δv₁≧1 but where ΔT₁≠ΔT or Δv₁≠Δv (ΔT and Δv fixed) from theparticles having duration ΔT and spectral width Δv, and an elementarydecoder receiving only those particles satisfying the minimum staterelation (ΔT.Δv=1), wherein: the time width ΔT of the pulse is shiftedor not depending on the value of the bits to be encoded and the spectralwidth Δv thereof, where Δt=ΔT−1t1−t01, the decoder then comprising: thefilter for the particles of the pulses of spectral width Δv, at leastone first particle counter: which is activated on one or two timeobservation windows of the bit reception period of duration Tb: ift0<t1, the first time observation window starts at instant t0(inclusive) and ends at instant t1 (exclusive), the second observationwindow starts at instant t1+Δt (exclusive) and ends at instant t1+T(inclusive); if t1<t0, the first time observation window starts atinstant t1 (inclusive) and ends at instant t0 (exclusive), the secondobservation window starts at instant t0+Δt (exclusive) and ends atinstant t0+T (inclusive); which is used to detect the presence or not ofparticles in the time observation window(s) and generate: a bit of value“0”:  if t0<t1, when a particle is detected in the window starting at t0of period k,  if t1<t0, when a particle is detected in the windowstarting at t0+Δt of period k, a bit of value “1”:  if t1<t0, when aparticle is detected in the window starting at t1 of period k,  ift0<t1, when a particle is detected in the window starting at t1+Δt ofperiod k, a signal indicating an ambiguity on the bit value if noparticle was detected in the first in the second observation window,and/or the first particle counter generating the number of particlesN_(Δv) which the particle counter detects and the decoder comprises, inaddition, at least: a second counter generating the number of particlesN_(Δf) received by the decoder and of spectral widths Δf different fromΔf≠Δv, and a comparator of these two numbers N_(Δv) and N_(Δf) such thatif N_(Δv)<<N_(Δf), the comparator generates a predetermined signalindicating either the ambiguity on the bit value or interception ofparticles by a third party.